US 6768744 B1 Abstract Generalized Processor Sharing (GPS) is a scheduling discipline which provides minimum service guarantees as well as fair resource sharing. The performance of GPS is governed by the scheduling weights associated with individual connections. The system discloses methods for GPS scheduling that handle an arbitrary number of connection classes and reservation-based weights and admission control techniques to achieve fairness among connection classes. The methods allow statistical multiplexing gains in the presence of multiple traffic and Quality of Service (QoS) classes of connections that share a common trunk. Also disclosed are several novel techniques to compute and adapt the weights.
Claims(43) 1. A generalized processor sharing (GPS) scheduler for allocating output bandwidth of said scheduler for a plurality of input connections comprising three or more classes of connections, each class of connections belonging to an associated quality of service class, there being one quality of service class for each class of connections, wherein each class of connections represents a different data type, comprising:
buffers for buffering each input connection;
memory for storing an initial predetermined connection weight for each input connection;
means for allocating a fraction of said output bandwidth to each input connection of each class of connections based on the initial connection weight stored for each input connection;
means for measuring the fraction of said output bandwidth used by each class of connections; and
means for adjusting the initial connection weight for each input connection to the extent possible consistent with maintaining a minimum quality of service (QoS) level for the quality of service class with which each class of connections is associated.
2. The GPS scheduler of
3. The GPS scheduler of
4. The GPS scheduler of
5. The GPS scheduler of
6. A generalized processor sharing (GPS) scheduler for allocating output bandwidth for an arbitrary number of input classes of connections, each class of connections belonging to an associated quality of service class, there being one quality of service class for each class of connections, wherein each class of connections represents a different data type, comprising:
buffers for buffering the input connections;
memory for storing an initial predetermined connection weight for each input connection;
means for allocating a fraction of said output bandwidth to each input connection of each class of connections based on the initial connection weight stored for each input connection;
means for measuring the fraction of said output bandwidth used by each class of connections; and
means for adjusting the initial connection weight for each input connection while maintaining a predetermined minimum quality of service (QoS) level for the quality of service class with which each class of connections is associated.
7. The GPS scheduler of
8. The GPS scheduler of
9. The GPS scheduler of
10. The GPS scheduler of
11. A generalized processor sharing (GPS) scheduler for allocating output bandwidth of said scheduler for a plurality of input connections comprising three or more classes of connections, each class of connections belonging to an associated quality of service class, there being one quality of service class for each class of connections, wherein each class of connections represents a different data type, comprising:
a plurality of buffers for buffering the input connections;
memory for storing an initial predetermined connection weight for each input connection;
means for allocating a fraction of said output bandwidth to each input connection of each class of connections based on the initial connection weight stored for each input connection;
means for measuring the fraction of said output bandwidth used by each class of connections; and
means for automatically adjusting the initial connection weight for each input connection to maintain a minimum quality of service (QoS) level for the quality of service class with which each class of connections is associated.
12. The GPS scheduler of
13. The GPS scheduler of
14. The GPS scheduler of
15. The GPS scheduler of
16. A method for generalized processor sharing (GPS) scheduling and network control, wherein j (j=1, 2, 3) classes of connections, each class of connections belonging to an associated quality of service class, there being one quality of service class for each class of connections, are presented to a GPS scheduler at a node with a total link bandwidth C, each class j comprising K
_{j }connections, and characterized by a quality of service (QOS) loss probability L_{j}, and a lossless multiplexing bandwidth e_{0} ^{j }and an activity factor a_{j}, each connection having an associated buffer and an allocated weight φ_{j }that determines said share of bandwidth C allocated to said connection, the method comprising the steps of:computing the number of connections K
_{1 }in a first class of connections, and the weight φ_{1 }associated with each connection in the first class of connections, the weight φ_{1 }being the weight needed to achieve the quality of service associated with the quality of service class to which the first class of connections belongs; computing the number of connections K
_{2 }in a second class of connections, and the weight φ_{2 }associated with each connection in the second class of connections, the weight φ_{2 }being the weight needed to achieve the quality of service associated with the quality of service class to which the second class of connections belongs; computing the number of connections K
_{3 }in a third class of connections, and the weight φ_{3 }associated with each connection in the third class of connections, the weight φ_{3 }being the weight needed to achieve the quality of service associated with the quality of service class to which the third class of connections belongs. 17. The method of
_{j}, such that the following expressions are satisfied: for all k (1≦k≦J), wherein ξ
_{i} ^{(j) }are independent binary random variables that represent the activity indicator for the i^{th }connection of class j that takes the value 1 if the connection is active, and 0 otherwise, and a_{j }is the fraction of time that the corresponding buffer and bandwidth is utilized for the i^{th }connection of class j.18. The method of
_{n }in an n^{th }class of connections, and the weight φ_{n }associated with each connection in the n^{th }class of connections.19. A method for GPS scheduling and network control utilizing the central limit theorem, wherein N classes of connections are presented to a GPS scheduler at a node with a total link bandwidth C, each class j comprising K
_{j }connections, each class of connections belonging to an associated quality of service class characterized by a quality of service (QoS) loss probability L_{j}, a lossless multiplexing bandwidth e^{j} _{0 }and an activity factor a_{j}, each connection having an associated buffer and allocated weight φ_{j }that determines the share of bandwidth allocated to the connection class, the method comprising the steps of:computing the weight assignments φ
_{j }needed to achieve the quality of service associated with the quality of service class to which for each class belongs and supportable population vectors K, such that the following expression is satisfied; where the vector η denotes the traffic mix and each value of K is the largest value of K possible for a given η;
computing the sum of the activity indicators a
_{j }for each class k as normally distributed, such that the following expression is satisfied, where U
_{j }is normally distributed with mean of 0 and variance of 1; computing the mean m
_{j }and the variance v_{j }of the bandwidth usage for each connection class j, and the weight φ_{j }of said connection class, such that the following expressions are satisfied: m _{j} =e _{j} ^{0} a _{j}, a _{j}=(e _{j} ^{0})^{2} a _{j}(1−a _{j}), where the connection class independent global parameter Δ is the unique positive solution of the cubic expression; and
allocating bandwidth to each class of connections according to the weights φ
_{j}. 21. A generalized processor sharing (GPS) scheduler for allocating output bandwidth of said scheduler for a plurality of input connections comprising three or more classes of connections, each class of connections belonging to an associated quality of service class, there being one quality of service class for each class of connections, wherein each class of connections represents a different data type, comprising:
buffers for buffering each input connection;
memory for storing an initial predetermined connection weight for each input connection;
means for measuring the fraction of said output bandwidth used by each class of connections; and
means for adjusting the initial connection weight for each input connection to the extent possible consistent with maintaining a minimum quality of service (QoS) level for the quality of service class with which each class of connections is associated.
22. The GPS scheduler of
23. The GPS scheduler of
24. The GPS scheduler of
25. The GPS scheduler of
26. A generalized processor sharing (GPS) scheduler for allocating output bandwidth for an arbitrary number of input classes of connections, each class of connections belonging to an associated quality of service class, there being one quality of service class for each class of connections, wherein each class of connections represents a different data type, comprising:
buffers for buffering the input connections;
memory for storing an initial predetermined connection weight for each input connection;
means for measuring the fraction of said output bandwidth used by each class of connections; and
means for adjusting the initial connection weight for each input connection while maintaining a predetermined minimum quality of service (QoS) level for the quality of service class with which each class of connections is associated.
27. The GPS scheduler of
28. The GPS scheduler of
29. The GPS scheduler of
30. The GPS scheduler of
31. A generalized processor sharing (GPS) scheduler for allocating output bandwidth of said scheduler for a plurality of input connections comprising three or more classes of connections, each class of connections belonging to an associated quality of service class, there being one quality of service class for each class of connections, wherein each class of connections represents a different data type, comprising:
a plurality of buffers for buffering the input connections;
memory for storing an initial predetermined connection weight for each input connection;
means for measuring the fraction of said output bandwidth used by each class of connections; and
means for iteratively and automatically adjusting the initial connection weight for each input connection to maintain a minimum quality of service (QoS) level for the quality of service class with which each class of connections is associated.
32. The GPS scheduler of
33. The GPS scheduler of
34. The GPS scheduler of
35. The GPS scheduler of
36. A method for generalized processor sharing (GPS) scheduling and network control, wherein j (j=1, 2, 3) classes of connections arc presented to a GPS scheduler at a node with a total link bandwidth C, each class j comprising K
_{j }connections, each class of connections belonging to an associated quality of service class, there being one quality of service class for each class of connections, each quality of service class being characterized by a quality of service (QoS) loss probability L_{j}, and a lossless multiplexing bandwidth e_{0j }and an activity factor a_{j}, each connection having an associated buffer and an allocated weight φ_{j }that determines said share of bandwidth C allocated to said connection, the method comprising the steps of:computing the number of connections K
_{1 }in a first class of connections, and the weight φ_{1 }associated with each connection in the first class of connections, the weight φ_{1 }being the weight needed to achieve the quality of service associated with the quality of service class to which the first class of connections belongs; computing the number of connections K
_{2 }in a second class of connections, and the weight φ_{2 }associated with each connection in the second class of connections, the weight φ_{2 }being the weight needed to achieve the quality of service associated with the quality of service class to which the second class of connections belongs; and computing the number of connections K
_{3 }in a third class of connections, and the weight φ_{3 }associated with each connection in the third class of connections, the weight φ_{3 }being the weight needed to achieve the quality of service associated with the quality of service class to which the first class of connections belongs. 37. The method of
_{j}, such that the following expressions are satisfied: for all k (1≦k≦J), wherein ξ
_{i} ^{(j) }are independent binary random variables that represent the activity indicator for the i^{th }connection of class j that takes the value 1 if the connection is active, and 0 otherwise, and a_{j }is the fraction of time that the corresponding buffer and bandwidth is utilized for the i^{th }connection of class j.38. The method of
_{n }in an n^{th }class of connections, and the weight φ_{n }associated with each connection in the n^{th }class of connections.39. A method for GPS scheduling and network control utilizing the central limit theorem, wherein N classes of connections are presented to a GPS scheduler at a node with a total link bandwidth C, each class j comprising K
_{j }connections, each class j having an associated quality of service class, there being one quality of service class for each class j, each quality of service class being characterized by a quality of service (QoS) loss probability L_{j}, a lossless multiplexing bandwidth e^{j} _{0 }and an activity factor a_{j}, each connection having an associated buffer and allocated weight φ_{j }that determines the share of bandwidth allocated to the connection, the method comprising the steps of:computing the weight assignments φ
_{j }for each class and supportable population vectors K, such that the following expression is satisfied: where the vector η denotes the traffic mix and each value of K is the largest value of K possible for a given η;
computing a sum of the activity indicators a
_{j }for each class k as normally distributed, such that the following expression is satisfied: where U
_{j }is normally distributed with mean of 0 and variance of 1; computing the mean m
_{j }and the variance v_{j }of the bandwidth usage for each connection class j, and the weight φ_{j }of said connection class, such that the following expressions are satisfied: m _{j} =e _{j} ^{0} a _{j},a _{j}=(e _{j} ^{0})^{2} a _{j}(1−a _{j}), where the connection class independent global parameter Δ is the unique positive solution of the cubic expression; and
allocating the available bandwidth among the classes according to the weight φ
_{j }associated with each class. 41. An iterative method for determining a GPS weight φ
_{k }in response to a change in the traffic mix of an arbitrary number of connection classes k as limit of the realizable region is reached and for determining a connection class to be admitted, the connection class to be admitted being the class having weight φ_{k}, the method comprising the steps of: setting an initial traffic vector K=(K_{1}, . . . , K_{k}), the values of (K_{1}, . . . K_{k}) being arbitrarily chosen, for K connections of each of an arbitrary number of connection classes k, each connection class belonging to an associated quality of service class, there being one quality of service class for each class of connections;setting an optimal weight φ
_{k }and an optimal global parameter Δ characterizing the realizable region; for each decision as to whether to admit a connection, evaluating the expression
where F
_{j}(φ_{j}) is a log moment generating function; if the expression is true, admitting the connection;
if the expression is not true, calculating new values for Δ and φ and the maximum allowable number of connections;
if the maximum number of allowable connections has not been reached, resetting the value of φ to the new value and admitting the connection; and
if the maximum number of connections has been reached, rejecting the connection.
42. An iterative method for choosing GPS weights φ
_{k }for an arbitrary number of classes of connections, each class of connections belonging to an associated quality of service class, there being one quality of service class for each class of connections, the method comprising the steps of:(a) choosing an initial feasible weight φ
^{(0)}; (b) setting a step counter n to a value of 1;
(c) computing a value for k, such that the following expression is satisfied:
(d) computing a subsequent weight φ
^{(n+1) }by subtracting the quantity τe_{k }from the weight φ^{(n+1)}; (e) computing a subsequent variable s
_{k }such that the following expression is satisfied: (f) computing the value
(g) if all H
_{k }are not equal, returning to step (c); (h) if all H
_{k }are equal, proceeding to step (i); and (i) allocating bandwidth among connections according to the computed values for the weights φ
_{k}. 43. A processor sharing node adapted for use as a GPS scheduler and network controller, said processor sharing node comprising:
input connections from a network for three input classes of connections, each class of connections belonging to an associated quality of service class, there being one quality of service class for each class of connections;
an output connection for connecting to a network;
a memory utilized to store weights to be applied to each of said classes of connections to determine the fraction of output bandwidth to allocate to each class of connections;
a processor utilized to measure the fraction of output bandwidth utilized by each of the three classes of connections, said processor further utilized to apply statistical methods to the measured fraction of output bandwidth utilized by each of the three classes of connections and to adjust the weights applied to each of said classes of connections to provide a minimum quality of service (QoS) to the quality of service class with which each class of connections is associated.
Description The present invention relates generally to improved methods and apparatus for regulating traffic in a communication network. In particular, the invention relates to the advantageous management of communication networks supporting multiple quality of service (QoS) classes utilizing generalized processor sharing (GPS) schedulers. In the present invention, GPS schedulers employing statistical methods allow efficient multiplexing of heterogeneous QoS classes. A simple communication network is comprised of nodes and endpoints, and links that connect individual nodes to other nodes and endpoints. Endpoints may be voice, data, text or video devices such as telephone sets, computers, fax machines, and the like. Individual links transmit voice, data, text, and video signals from endpoints to nodes, and between various nodes within a given communication network. Typically, each link is bi-directional, capable of carrying signals in a forward and reverse direction. Each link is characterized by certain bandwidth parameters that are a measure of a given link's capacity in each direction. Nodes typically include buffers, thereby enabling temporary storage of network traffic at that node. If a given link has insufficient bandwidth to carry the traffic received by that node at a given time, the buffer may be used to store the received traffic until the link can handle the stored traffic. The explosive growth of consumer demand for Internet access, as well as other network applications, has resulted in a commensurate demand for additional bandwidth in high speed communication networks. The growth in available bandwidth has led to the development of a wide variety of applications with diverse QoS requirements, such as maximum allowable transmission delay and loss of information content, as well as bandwidth characteristics. Despite the growth of available capacity, bandwidth resource management still constitutes a challenge to network providers. The challenge is to provide a service level matched to the needs of a diversity of service requirements that network providers are contractually obligated to guarantee. One significant development in bandwidth resource management has been the utilization of large scale per virtual circuit (per VC) queuing in switch design, since it allows tight control over resource allocation and usage for each network connection. In this context, a virtual circuit (VC) is a connection in an asynchronous transfer mode (ATM) network that appears to the initiating and destination endpoints as a direct connection, regardless of the actual physical network path connecting those endpoints. GPS schedulers allow substantial network capacity sharing, as well as isolation and QoS guarantees, by assigning a weight to individual connections. These weight assignments are chosen to closely correlate to the actual network traffic characteristics and QoS requirements. Higher weight connections are given a larger proportion of the available bandwidth than lower weight connections in order to maintain the QoS requirements of the particular network. The present invention relates to advantageous methods and apparatus for bandwidth resource management in the implementation of GPS schedulers. GPS schedulers allow substantial network sharing capacity, as well as isolation and QoS guarantees. These advantageous properties of GPS schedulers are the result of the proper design of the weights assigned to individual network connections. The weights assigned are closely correlated to the characteristics of the actual network traffic as well as the QoS required for each network connection. In one aspect, the methods disclosed by the present invention allow an arbitrary number of QoS classes of service for an arbitrary number of class connections on a common trunk. In one embodiment, a central limit approximation, based on the central limit theorem, is used to model the aggregate activity of the connections. The performance of the GPS scheduler is governed by the scheduling weights associated with the individual connections. The weight selection for any given connection is formulated as a nonlinear set of algebraic equations. In another embodiment, a Chernoff approximation is applied in a similar manner. The present invention is applicable to worst-case dual leaky bucket regulated (DLBR) connections, in which connections are classified by their leaky bucket parameters. The QoS is specified by the probability of violating the delay bound, where the probability and delay bound are QoS parameters associated with each connection class. Multiplexing gains are obtained by assuming that the regulated sources are independent and noncolluding. In another aspect, the present invention provides an advantageous technique based on a reservation mechanism for the slow adaptation of weights, which may also be implemented by switching among a small set of precomputed weights. The technique of the present invention enforces fairness among connections with varying resource requirements, which is an important requirement of connection admission control (CAC). A more complete understanding of the present invention, as well as further features and advantages, will be apparent from the following Detailed Description and the accompanying drawings. FIG. 1A illustrates an output-buffer switch utilizing a GPS scheduler; FIG. 1B illustrates a multi-class GPS scheduler at a node in accordance with the present invention; FIGS. 2A, FIGS. 3A, FIGS. 4A, FIGS. 5A, FIG. 6 illustrates the realizable region for a number of connections of classes K FIG. 7 illustrates a process for iteratively solving for the optimizing values of weights {φ FIGS. 8A, FIGS. 9A, FIG. 10 illustrates a process for a necessity based connection admission control method in accordance with one embodiment of the present invention; and FIG. 11 illustrates a process for a virtual partitioning based connection admission control method in accordance with one embodiment of the present invention. The present invention deals with the characteristics of the capacity region of a multi-class GPS scheduler, and discloses methods for controlling, in real time, the GPS weights that maximize network bandwidth capacity. That is, the GPS scheduler of the present invention maximizes the capacity of an output link by utilizing advantageous methods to assign GPS weights to different classes of connections in real time. These advantageous methods are described in further detail below. Of particular importance are two approaches for controlling GPS weights which are based on the central limit and large deviation regimes. These large deviation regimes logically give rise to the Gaussian and the Chernoff asymptotic approximations. The central limit approximation is applicable when the violation probabilities are relatively high, typically 10 FIG. 1A illustrates a 2×2 output-buffer switch The details of a system A typical dual leaky bucket regulator has parameters (r, P, B The advantages of the disclosed methods of GPS scheduling are shown in the following experimental results and illustrated in FIGS. 2A, Example 1: Source connection classes 1 & 2. Example 2: Source connection classes 3 & 4. Example 3: Source connection classes 5 & 6. Example 4: Source connection classes 4, 5 & 6. Note that the source characteristics of the 6 classes as shown in Table 1 correspond to voice for class 5, while the remaining classes represent various classes of data.
For each of the four examples listed above, the realizable region for each of the following cases are plotted: Case 1: No statistical multiplexing, i.e. Σ Case 2: The mean value approximation, i.e. Σ Case 3: The central limit approximation. Case 4: The basic Chernoff approximation. Case 5: The refined Chernoff approximation. For examples 1, 2 and 3 above, the following data are plotted. FIGS. 2A-2C illustrate the realizable region for a varying number of connections of two connection classes, K FIGS. 3A-3C illustrate the ratio of weights φ For comparison, FIGS. 4A-4C illustrate the exact realizable region FIG. 6 illustrates the 3-connection class example, where only the realizable region Simulation results for the real time connection admission control methods N-CAC and VP-CAC, as discussed below, are illustrated by FIGS. 8A-8C and FIGS. 9A-9C, respectively. The simulations were run for 2 different QoS classes, class 1 and class 2 as shown in Table 1 above, utilizing Poisson connection traffic, that is, Poisson connection arrivals with exponentially distributed holding times. The arrival rates λ were fixed at a 3:1 ratio. A nominal load measure: is defined with respect to which all performance measures are plotted. FIGS. 8A-8B illustrate the load factor for class 1 and class 2 connections respectively utilizing the N-CAC method described further below. FIGS. 9A-9B illustrate the load factor for class 1 and class 2 connections respectively, utilizing the VP-CAC method described further below. In each simulation, the number of carried connections of each class was varied as shown. FIG. In the case of the VP-CAC method, the desired traffic mix η* was determined using the ratio of arrivals to departures for each QoS class. For each data point, the simulation was run for a long enough period of time to eliminate the initial transient behavior, after which the data shown were collected. FIGS. 8A-8B illustrate the carried load FIG. 8C illustrates the frequency of weight changes In addition to the above, the simulations provided insight into the transient behavior of the VP-CAC method. In a typical implementation, the choice of the desired traffic mix may be determined by a forecast of the offered the traffic. Periodically, a new desired mix is computed to correspond to expected changes in traffic. As will be apparent from the discussion below, the GPS weights cannot be instantaneously changed to the weights that would properly correspond to the new desired traffic mix. Therefore, the transient behavior of the VP-CAC method in response to changes in the targeted mix is well adapted for use in this environment since the weight changes are quite smooth but rapid, requiring few weight changes. The discussion now turns to the description of the advantageous methods of GPS scheduling and connection admission control. It has been previously shown that in the extremal regulated connection process, the bandwidth demand to satisfy QoS is an on-off process taking values e In equation (1) below, e The activity indicator a is given by a=r/e The weight given to connections of class j in the GPS scheduler where ξ In considering statistical QoS, the extremal regulated connection processes have independent random phases. An extremal connection is the worst case connection that switches between on and off. As a consequence of this worst case condition, the activity indicators ξ
In the next example, consider one specific, or tagged, connection which is active, and assume, without loss of generality, that it is connection Equivalently: Hence, statistical QoS is satisfied for all extremal regulated connection processes if, for all k (1≦k≦J): Equation (5) gives the conditions to be satisfied for the set of connections given by K={K Of fundamental importance is the realizable set, or region, which is defined as the set of connection population vectors K for which there exists a set of weights {φ The vector η denotes the traffic mix and, for given η, the goal is to find the largest value of K that is realizable. In one embodiment, the present invention determines the realizable region utilizing the adapted Gaussian approximation. Calculation of the realizable region utilizing the adapted Gaussian approximation method requires a determination of the bounds for characterizing the realizable region. A simple and conservative bound for the realizable region may be obtained by a mean value approximation by assuming all connections are active all the time: At the other extreme, a rough optimistic estimate of the realizable region is obtained by using mean values of the activity indicators, Using mean values for the condition invoked in the right hand side of equation (4) gives: The corresponding realizable region is a simplex: with the weights φ In another embodiment, the present invention determines the realizable region utilizing the adapted central limit approximation. In this manner, the adapted central limit theorem for {K where U where U=N(0,1) and satisfies the following equality in distributions: Introducing the mean and variance of the extremal regulated connection processes discussed above:
And allowing: Then, from equation (11), for k=1, . . . , J, From standard bounds on the tail behavior of the Gaussian distribution, equation (15) yields: Here is a close, conservative approximation which is also asymptotically exact as the loss probability approaches zero, L Equation (16) can be solved by the following procedure to yield the result shown in equation (17) below. Starting with equation (16), and introducing the traffic mix η from equation (6) above to solve for k=1, 2, . . . , J, The value of interest is K The following lemma is now applied: Given N real-valued, continuous and differentiable functions {f the optimal solution to satisfies
for all k∈{1, 2, . . . , N} where x* is the optimizing vector. Referring back to equation (18), it should be clear that the solution must satisfy where Δ is a constant, for the case where k=1, 2, . . . , J. Utilizing equation (22): Therefore, upon introducing the traffic mix η into equation (14) above, and further, Substituting from equations (22) and (25) above, From equations (23) and (26), This computation yields equation (29) below, while equation (28) below is obtained from equation (22). It is straightforward to show that the above cubic equation in Δ has a unique positive solution. Finally, equation (30) follows from equation (26). Equation (16) above now yields: where Δ is the unique positive solution of the following cubic equation: This result is an approximation based on the Gaussian approximation. Note that the parameter Δ depends on the connection populations {K The realizable region of connection population vectors K is now given by: which may be contrasted with equation (9). Since Δ depends on {K An alternative approach to calculating the realizable region utilizing a Chernoff approximation is discussed further below. Calculation of the realizable region by the Chernoff approximation requires a determination of the bounds for characterizing the realizable region. A basic bound that holds for any random variable with a well defined moment generating function is calculated as:
for all s≧0, where F(s) is the log moment generating function of the random variable x, defined as:
with s[ ] denoting the expected value. In particular, the tightest value of this bound is obtained thus: Equation (33) determines the Chernoff bound, which is also asymptotically tight when x is the sum of a large number of independent random variables, where the number, as a proportion of C, is bounded as C→∞. Defining M where
is the log moment generating function of the binary activity indicators ξ for some s Equation (37) therefore yields the values of the weights {φ Equation (37) is difficult to solve analytically, as well as numerically. The following calculations focus on approximate solutions which realize subsets of together with the GPS weights. In equation (36), the selection all s which leads to the reduced problem where Applying the lemma of equation (19) again, it can be shown that for a given η, the maximizing weight vector in this reduced problem satisfies
for some class-independent global parameter Ω. This result then implies, from equation (40),
where Δ is yet another class independent parameter. Therefore, the solution is: with Δ given by Equations (43) and (44) provide a relatively simple approximate solution to the problem stated in equation (37). The maximization in equation (3442), which is the key step in the approximation, is one-dimensional, with a unique solution that follows from convexity, and the computation of Δ is straightforward. The performances of the approximate solutions obtained from equations (43) and (44) have been tested in several non-homogeneous examples. The results, which are shown in FIGS. 2, An iterative technique for solving equation (37) is disclosed based on the Chernoff approximation, which is a refinement to the solution given by equations (43) and (44). The key distinguishing feature to this refinement is that the parameters {s The following two properties of equations (45) and (46) are straightforward to prove. First, the functions H for all classes k, with the superscript * while referring to the optimizing values as before. These properties of the optimal solution are exploited in the following iterative process FIG. 7 illustrates an iterative process At process step At process step
where and where e At process step At process step In another embodiment, the present invention further discloses advantageous methods and apparatus to perform adaptive weight control and adaptive connection admission control (CAC) in real time. In the discussion below, it is assumed that connections are not queued. In other words, connections are accepted or rejected immediately upon arrival. The CAC methods described depend heavily on the shape of the realizable region derived above, and can be applied to either of the two approximations described above. The following discussion addresses the Chernoff based approximate solution of the present invention. A very similar procedure may be readily applied for the Gaussian based approximation solution. One embodiment of the present invention discloses a straightforward, greedy procedure that operates on the philosophy of avoiding weight changes unless necessary. In a typical real world implementation, it is desirable that the frequency of weight changes is small. In this case, “necessary” CAC should be interpreted to mean that without a weight change, the incoming connection cannot be accommodated. In the following discussion, the realizable region is characterized by a single class independent global parameter Δ which also determines all the weights. Therefore, only parameter Δ need be adapted as opposed to the N-dimensional weight vector φ, which is a convenient feature for implementation. Upon substituting equation (43) into equation (38), the following compact characterization of the approximate realizable region for fixed weights {φ Note that in the case of the Gaussian approximation, the corresponding characterization is given by solving equation (30). In another embodiment of the present invention, a “necessity-based” connection admission control (N-CAC) process The process
is not true, the process proceeds to step
is evaluated. If the expression is true, the process proceeds to step
is not true, then the connection is rejected, the process proceeds to step The connection blocking performance of the N-CAC method is discussed below. The connection blocking performance of the method may be obtained from standard traffic models in which the state space is the realizable region. For Poisson traffic, with blocked connections cleared, the solution to this model is product form. In other words, the blocking probability B where λ Relative to other VP based methods, the methods of the present invention utilize nominal allocations for each connection class, and reservations against classes that exceed their nominal allocations. The method then performs the following steps to admit an arriving connection of class k. The VP connection admission control (VP-CAC) process The process As stated above, the method reserves a capacity corresponding to that required to admit a single connection of any under loaded class in the system. Reservation for more than a single However, the N-CAC method has several drawbacks. First, as demonstrated later in the numerical results, the method is unfair towards connections requiring greater resources in terms of longer holding times or greater bandwidth. These connections are quickly squeezed out by the connections requiring less resources when the system is heavily loaded. Second, the weight changes are performed in a greedy manner, with no attention given to meeting class dependent blocking targets. Third, the method sometimes exhibits flapping, where the system reacts strongly to temporary traffic fluctuations, and does not settle into a steady state. The results of simulations utilizing the method of process Therefore, a new method with superior performance, especially with regard to fairness, is disclosed. In this case, a “desirable” connection mix vector η* is assumed to be targeted when the system is heavily loaded. This vector may, for instance, be obtained by considerations of revenue maximization combined with considerations of fairness, such as meeting maximum blocking requirements for each class, for specified offered traffic. The method is effectively insensitive to η* when the system is lightly loaded, while gracefully enforcing the mix η* as the load becomes heavier. Such mechanisms have been proposed before in other contexts using the method of virtual partitioning (VP) described in other references and incorporated herein. See, for example, D. Mitra and I. Ziedins, “Virtual Partitioning by Dynamic Priorities: Fair and Efficient Resource Sharing by Several Services”, Broadband Communications, Proceedings of the International Zurich Seminar on Digital Communications, 1976, pp. 173-185, S. Borst and D. Mitra, “Virtual Partitioning for Resource Sharing by State-Dependent Priorities: Analysis, Approximations and Performance for Heterogeneous Traffic”, Teletraffic Contributions for the Information Age, Proc. ITC-15, 1997, pp. 1457-1468, and K. Kumaran and D. Mitra, such call, for purposes of increased protection, may also be considered. However, as discussed below, this is typically not necessary since reservation for a single connection enforces fairness effectively. As is to be expected, all the properties associated with robust and efficient resource sharing described in previous work on VP apply here. As intended, the method achieves the goal of unfettered sharing at light loads and drifts towards the intended traffic mix η* at heavy loads. The results of simulations utilizing the method of process While the present invention is disclosed in the context of a presently preferred embodiment, it will be recognized that a wide variety of implementations may be employed by persons or ordinary skill in the art consistent with the above discussion and the claims that follow below. Patent Citations
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